By Sir Thomas Heath
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Additional info for A History of Greek Mathematics, Vol. 1: From Thales to Euclid
Since then the subject has been very greatly advanced; new texts have been published, important new documents have been discovered, and researches by scholars and mathematicians in different countries have thrown light on many obscure points. It is, therefore, high time for the complete story to be rewritten. It is true that in recent years a number of attractive histories of mathematics have been published in England and America, but these have only dealt with Greek mathematics as part of the larger subject, and in consequence the writers have been precluded, by considerations of space alone, from presenting the work of the Greeks in sufficient detail.
32 Canonic is the theory of the musical intervals as expounded in works like Euclid’s κατατομὴ κανόνος, Division of the canon. 33 (1) The first is Optics proper, the business of which is to explain why things appear to be of different sizes or different shapes according to the way in which they are placed and the distances at which they are seen. Euclid’s Optics consists mainly of propositions of this kind; a circle seen edgewise looks like a straight line (Prop. 22), a cylinder seen by one eye appears less than half a cylinder (Prop.
PYTHAGOREAN GEOMETRY Pythagoras Discoveries attributed to the Pythagoreans (α) Equality of sum of angles of any triangle to two right angles (β) The ‘Theorem of Pythagoras’ (γ) Application of areas and geometrical algebra (solution of quadratic equations) (δ) The irrational () The five regular solids (ζ) Pythagorean astronomy Recapitulation VI. PROGRESS IN THE ELEMENTS DOWN TO PLATO’S TIME Extract from Proclus’s summary Anaxagoras Oenopides of Chios Democritus Hippias of Elis Hippocrates of Chios (α) Hippocrates’s quadrature of lunes (β) Reduction of the problem of doubling the cube to the finding of two mean proportionals (γ) The Elements as known to Hippocrates Theodorus of Cyrene Theaetetus Archytas Summary VII.
A History of Greek Mathematics, Vol. 1: From Thales to Euclid by Sir Thomas Heath